{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Maximum cut problem "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The MaxCut problem is one of the most famous NP-complete problems in combinatorial optimization. Given an undirected graph $G(V, E)$ with a vertex set $V$ and an edge set $E$, the Max Cut problem seeks to partition $V$ into two sets such that the number of edges between the two sets (considered to be severed by the cut), is a large as possible. Applications can be found (for example) in clustering problems for marketing purposes or portfolio optimization problems in finance."
   ]
  },
  {
   "attachments": {
    "image-2.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![image-2.png](attachment:image-2.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solving MaxCut on DWave  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Imports \n",
    "import boto3\n",
    "import numpy as np\n",
    "import json\n",
    "from braket.aws import AwsDevice\n",
    "from braket.ocean_plugin import BraketSampler, BraketDWaveSampler\n",
    "\n",
    "import networkx as nx\n",
    "import dwave_networkx as dnx\n",
    "from dimod.binary_quadratic_model import BinaryQuadraticModel\n",
    "from dwave.system.composites import EmbeddingComposite\n",
    "from collections import defaultdict\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "# magic word for producing visualizations in notebook\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# S3 destination\n",
    "my_bucket = f\"amazon-braket-xxx\"#\"amazon-braket-xxx\" # the name of the bucket\n",
    "my_prefix = \"maxcut-output\" # the name of the folder in the bucket\n",
    "s3_folder = (my_bucket, my_prefix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Device: Device('name': DW_2000Q_6, 'arn': arn:aws:braket:::device/qpu/d-wave/DW_2000Q_6)\n"
     ]
    }
   ],
   "source": [
    "# Setting up the backend\n",
    "device = AwsDevice(\"arn:aws:braket:::device/qpu/d-wave/DW_2000Q_6\")\n",
    "print('Device:', device)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# helper function to plot graph\n",
    "def get_graph(graph, pos):\n",
    "    \"\"\"\n",
    "    plot colored graph for given solution\n",
    "    \"\"\"\n",
    "   # nodes\n",
    "    nx.draw_networkx_nodes(graph, pos, node_size=700)\n",
    "\n",
    "    # edges\n",
    "    nx.draw_networkx_edges(graph, pos)\n",
    "\n",
    "    # labels\n",
    "    nx.draw_networkx_labels(graph, pos, font_size=20, font_family='sans-serif')\n",
    "\n",
    "    # plot the graph\n",
    "    plt.axis('off')\n",
    "    plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Setting up the graph for DWave"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Create empty graph\n",
    "G = nx.Graph()\n",
    "\n",
    "# Add edges to the graph (also adds nodes)\n",
    "G.add_edges_from([(1,2),(1,4),(1,5),(2,3),(3,4)])\n",
    "\n",
    "# plot graph\n",
    "pos = nx.spring_layout(G)\n",
    "# plot graph with labels\n",
    "get_graph(G, pos)\n",
    "\n",
    "# ------- Set up our QUBO dictionary -------\n",
    "# Initialize our Q matrix\n",
    "Q = defaultdict(int)\n",
    "\n",
    "# Update Q matrix for every edge in the graph\n",
    "for u, v in G.edges:\n",
    "    Q[(u,u)]+= -1\n",
    "    Q[(v,v)]+= -1\n",
    "    Q[(u,v)]+= 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Running QUBO on DWave"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "------------------------------------------------------------\n",
      "          Set 0          Set 1    Energy        Cut Size    \n",
      "------------------------------------------------------------\n",
      "      [2, 4, 5]         [1, 3]     -5.0             5       \n",
      "         [1, 3]      [2, 4, 5]     -5.0             5       \n",
      "\n",
      "Your plot is saved to maxcut_plot.png\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Set up DWave parameters\n",
    "chainstrength = 8\n",
    "numruns = 100\n",
    "\n",
    "# Run the QUBO on the Braket solver from your config file\n",
    "# set sampler\n",
    "sampler = BraketDWaveSampler(s3_folder,'arn:aws:braket:::device/qpu/d-wave/DW_2000Q_6')\n",
    "sampler = EmbeddingComposite(sampler)\n",
    "response = sampler.sample_qubo(Q, chain_strength=chainstrength, num_reads=numruns)\n",
    "energies = iter(response.data())\n",
    "\n",
    "# ------- Print results to user -------\n",
    "print('-' * 60)\n",
    "print('{:>15s}{:>15s}{:^15s}{:^15s}'.format('Set 0','Set 1','Energy','Cut Size'))\n",
    "print('-' * 60)\n",
    "for line in response:\n",
    "    S0 = [k for k,v in line.items() if v == 0]\n",
    "    S1 = [k for k,v in line.items() if v == 1]\n",
    "    E = next(energies).energy\n",
    "    print('{:>15s}{:>15s}{:^15s}{:^15s}'.format(str(S0),str(S1),str(E),str(int(-1*E))))\n",
    "\n",
    "# ------- Display results to user -------\n",
    "# Grab best result\n",
    "# Note: \"best\" result is the result with the lowest energy\n",
    "# Note2: the look up table (lut) is a dictionary, where the key is the node index\n",
    "#   and the value is the set label. For example, lut[5] = 1, indicates that\n",
    "#   node 5 is in set 1 (S1).\n",
    "lut = response.lowest().first.sample\n",
    "\n",
    "# Interpret best result in terms of nodes and edges\n",
    "S0 = [node for node in G.nodes if not lut[node]]\n",
    "S1 = [node for node in G.nodes if lut[node]]\n",
    "cut_edges = [(u, v) for u, v in G.edges if lut[u]!=lut[v]]\n",
    "uncut_edges = [(u, v) for u, v in G.edges if lut[u]==lut[v]]\n",
    "\n",
    "# Display best result\n",
    "pos = nx.spring_layout(G)\n",
    "nx.draw_networkx_nodes(G, pos, nodelist=S0, node_color='r')\n",
    "nx.draw_networkx_nodes(G, pos, nodelist=S1, node_color='c')\n",
    "nx.draw_networkx_edges(G, pos, edgelist=cut_edges, style='dashdot', alpha=0.5, width=3)\n",
    "nx.draw_networkx_edges(G, pos, edgelist=uncut_edges, style='solid', width=3)\n",
    "nx.draw_networkx_labels(G, pos)\n",
    "\n",
    "filename = \"maxcut_plot.png\"\n",
    "plt.savefig(filename, bbox_inches='tight')\n",
    "print(\"\\nYour plot is saved to {}\".format(filename))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solving MaxCut using Quantum Approximate Optimization"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Quantum Approximate Optimization Algorithm (QAOA)__: MaxCut problem enjoys a natural mapping onto quantum Ising model. Using QAOA we would like to find the lowest energy state of the Hamiltonian encoding the optimization problem\n",
    "\n",
    "$$\\hat{H}_{C}=\\sum_{i>j} J_{i,j} \\sigma_{i}^{z} \\sigma_{j}^{z},$$\n",
    "\n",
    "which can be written as a matrix of size $(2^{N}, 2^{N})$ with diagonal elements only corresponding to all possible classical values for the cost function $H_{C}$. \n",
    "The ground state of $\\hat{H}_{C}$ corresponds to the optimal solution of the classical combinatorial problem.\n",
    "\n",
    "__QAOA ansatz__: Finding this ground state exactly is hard. \n",
    "To approximate this groundstate, QAOA prepares a parametrized ansatz state (corresponding to a parameterized  gate  sequence),  whose  parameters  are iteratively updated by a classical optimizer in a closed loop. \n",
    "Specifically, QAOA involves a specific ansatz wavefunction parametrized by a parameter family $(\\vec{\\beta}, \\vec{\\gamma})$, embedded into a larger classical optimization loop to find the optimal values for these parameters. \n",
    "As shown in Ref.[1], good approximate solutions to the problem class considered here can be found by preparing the variational state \n",
    "\n",
    "$$|\\gamma, \\beta \\rangle = U_{x}(\\beta_{p})U_{zz}(\\gamma_{p}) \\cdots U_{x}(\\beta_{1})U_{zz}(\\gamma_{1}) |s\\rangle$$\n",
    "\n",
    "with single qubit rotations induced by $U_{x}(\\beta) = \\exp(-i\\beta \\sum_{i}\\sigma_{i}^{x})$, \n",
    "and interactions described by $U_{zz}(\\gamma) = \\exp(-i\\gamma H_{C})$,\n",
    "starting initially from a product of $\\sigma^{x}$ eigenstates, i.e.,\n",
    "$|s\\rangle =|-,-,\\dots\\rangle$, with $|-\\rangle = (|0\\rangle -|1\\rangle  )/\\sqrt{2}$. \n",
    "The family of states $|\\gamma, \\beta \\rangle$ is prepared by alternating single-qubit operations $U_{x}(\\beta_{p})$ with targeted spin-spin interactions generated by the cost Hamiltonian $H_{C}$. \n",
    "The depth $p$ can be interpreted as a hyperparameter. \n",
    "For $p$ layers of QAOA blocks, there are $2p$ classical parameters to optimize over, \n",
    "since each layer $k$ is characterized by just two variational parameters, $\\gamma_{k}$ and $\\beta_{k}$. \n",
    "The preparation step outlined above is followed by a measurement in the computational basis, giving a classical string $z$, with which one can evaluate the objective function $H_{C}$ of the underlying combinatorial problem at hand. \n",
    "Taking several measurements shots one can build the expectation value $E(\\beta, \\gamma) = \\langle H_{C} \\rangle$ that we report as the objective function to the classical minimizer (while other choices could be possible as well). \n",
    "Repeating this procedure will provide an optimized string $z$, with the quality of the result improving as the depth of the quantum circuit $\\sim 2p$ is increased [1]. \n",
    "In fact, in principle (in the absence of noise and other imperfections), QAOA can reach the global optimum of any cost function in the limit $p \\rightarrow \\infty$ [1], approaching the adiabatic protocol. \n",
    "Thus, in theory the computational power of QAOA increases with $p$, but in practice the number of layers that can be executed without errors on NISQ devices is limited due noise and imperfections. \n",
    "\n",
    "__Optimization__: Since we are primarily interested in solving the classical optimization problem, within this routine it is sufficient to keep track of the best classical bitstring. \n",
    "This means that the wavefunction prepared by the quantum circuit $|\\gamma, \\beta \\rangle$ has to have some overlap with the optimal solution $|z^{*} \\rangle$ that we can read out as bitstring $z^{*}$ in the measurement shots. \n",
    "To this end, in principle (i.e., without any training), we could just sample from a completely uniform state that is prepared in a superposition of all computational basis states, as prepared by applying Hadamard gates to all qubits: $|\\mathrm{uniform}\\rangle = 1/\\sqrt{2^{N}}\\sum_{i}|z_{i}\\rangle$. \n",
    "In that case (assuming a single optimal solution) the success probability per shot amounts to $p_{\\mathrm{success}}=1/2^{N}$. \n",
    "We can then amplify our success chances by just taking many measurement shots. \n",
    "For large systems, however, this approach is not scalable as we would need to take an exponentially increasing number of measurements. \n",
    "That is why we train our circuits, update the parameters, with the goal to increase our success chances to find the optimal bitstring. \n",
    "We can quantify our success chances as follows [6]. \n",
    "For a given wavefunction $|\\gamma, \\beta \\rangle$ the probability to find the optimal solution in a single shot is given by \n",
    "\n",
    "$$ p_{\\mathrm{success}}(\\gamma, \\beta) = |\\langle z^{*}|\\gamma, \\beta \\rangle |^{2},$$\n",
    "\n",
    "where $z^{*}$ denotes the optimal bitstring. \n",
    "If we perform $M$ repeated measurements, the overall probability $P$ for observing this solution at least once is given by \n",
    "\n",
    "$$ P = 1 - (1-p_{\\mathrm{success}}(\\gamma, \\beta))^{M}, $$ \n",
    "\n",
    "since the term $(1-p_{\\mathrm{success}}(\\gamma, \\beta))^{M}$ gives the probability of _not_ obtaining $z^{*}$ in repeated $M$ trials. \n",
    "Therefore, to have an overall success chance up to $\\epsilon$ close to 100%, i.e., $P \\geq 1-\\epsilon$, the number of required shots has to be \n",
    "\n",
    "$$ M \\geq \\frac{\\log(\\epsilon)}{\\log(1-p_{\\mathrm{success}}(\\gamma, \\beta))}.$$\n",
    "\n",
    "Let us illustrate this results as follows: \n",
    "If we do not know anything and just resort to a uniform superposition $|\\mathrm{uniform}\\rangle$, for a small system with $N=10$ qubits we can find the optimal solutions with 80% success probability by taking at least $\\sim 1650$ shots. \n",
    "For just $N=20$ qubits, however, this number amounts to $\\sim 1.7 \\times 10^{6}$, making this naive approach unfeasible. \n",
    "Conversely, if we can train the quantum circuit to obtain $p_{\\mathrm{success}}(\\gamma, \\beta) \\sim 0.1$, we only need $\\sim 15$ shots to have $P\\geq 80\\%$. \n",
    "Below we will track and illustrate the best classical optimum as our algorithm proceeds towards a local or (ideally) global optimum.  \n",
    "\n",
    "__Objective function__: Finally, some more details on the definition of the cost function are in order. \n",
    "Following the standard approach [1, 4], QAOA tries to minimize the expectation value $\\langle \\hat{H}_{C} \\rangle$, but does _not_ explicitly maximize the success probability [6]. \n",
    "However, a low expectation value for $\\langle \\hat{H}_{C} \\rangle$ does not necessarily translate to a high success probability $p_{\\mathrm{success}}(\\gamma, \\beta)$, as can be understood from the following example:\n",
    "Consider (for example) a variational state that is a linear combination of low energy excited eigenstates of the cost Hamiltonian $\\hat{H}_{C}$ other than the ground state $|z^{*}\\rangle$. \n",
    "By definition, this state will have a relatively low expectation value $\\langle \\hat{H}_{C} \\rangle$ while the success probability is zero (as this low energy state does not have any overlap with the ground state). \n",
    "Similarly, a variational state that is a linear combination of the ground state with very high energy eigenstates could have a high success probability $p_{\\mathrm{success}}(\\gamma, \\beta)$, while (at the same time) reporting a high cost value to the classical optimizer.\n",
    "To address this issue, alternative methods for the optimization of the variational parameters have recently been proposed. \n",
    "While for simplicity we follow the majority of the literature and take $\\langle \\hat{H}_{C} \\rangle$ as cost value that we report to the classical optimizer, here we do mention a potential alternative for future research: \n",
    "One approach is to use the Gibbs objective function, defined as $\\mathrm{cost}=-\\mathrm{log} \\langle \\exp(-\\eta \\hat{H}_{C})\\rangle$, with the hyperparameter $\\eta>0$ [7]. \n",
    "As compared to the simple expectation value $\\langle \\hat{H}_{C} \\rangle$, this definition of the cost value shows stronger rewards for low energy states, thereby increasing the success probability. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#!pip install seaborn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Additional imports \n",
    "from scipy.optimize import minimize\n",
    "import time\n",
    "from datetime import datetime\n",
    "import seaborn as sns\n",
    "\n",
    "# AWS imports: Import Braket SDK modules\n",
    "import boto3\n",
    "from braket.circuits import Circuit, Observable\n",
    "from braket.aws import AwsSession, AwsDevice\n",
    "from braket.devices import LocalSimulator"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Set up device: Local Simulator\n",
    "#device = LocalSimulator()\n",
    "\n",
    "# set up the device to be the managed simulator\n",
    "device = AwsDevice(\"arn:aws:braket:::device/quantum-simulator/amazon/sv1\")\n",
    "\n",
    "# set up the device to be the IonQ quantum computer\n",
    "#device = AwsDevice(\"arn:aws:braket:::device/qpu/ionq/ionQdevice\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Setup the graph for QAOA "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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XTp48KbvdbjqO1zHxAV6Sn5+vO+64g9KD38vPz9ekSZMCsvQkig/wGp7CgEARyMucEkudgFeUlJTo4Ycf1pEjRxQeHm46DtBm586dU//+/XX8+HFFRUWZjtMumPgAL8jKytKzzz5L6cHvrV69WhMmTAjY0pO4VyfgsXPnzik3N1cHDhwwHQXwWG5urp588knTMdoVS52Ah/7whz+otLRUy5YtMx0F8MiFCxfUt29fVVVVKSYmxnScdsPEB3igublZOTk5euedd0xHATy2Zs0apaamBnTpSbzGB3hkzZo16tGjh1JSUkxHATyWl5cX0Ls5r2CpE/DAhAkT9C//8i/6wQ9+YDoK4JHa2lrdfvvtOnLkSMDfeYiJD2ij/fv3q6ysTI8++qjpKIDH3nvvPY0cOTLgS0+i+IA2y8rK0owZMwLyJr4IPsGyzCmx1Am0yYULF9S/f3+VlZWpd+/epuMAHqmvr1evXr108OBBxcbGmo7T7pj4gDZ47bXXNHHiREoPAaGgoEDDhg0LitKTOM4AuM3lcikrK0uvvfaa6SiAVwTTMqfExAe4raCgQF26dNGoUaNMRwE81tjYqDVr1mjq1Kmmo3QYig9w05WnMNhsNtNRAI9t2LBB8fHxQbVsz1In4IbDhw+ruLhYubm5pqMAXhFsy5wSuzoBtzz//POKiIjQ73//e9NRAI85nU716tVLO3bsUL9+/UzH6TBMfEAr1dbWatmyZdq1a5fpKIBXbNmyRXFxcUFVehKv8QGttnz5cqWmpgbdDwkErry8PKWlpZmO0eFY6gRawbIsJSYmKjMzU+PGjTMdB/BYc3Ozbr/9dn344YcaOHCg6TgdiokPaIVNmzZJksaOHWs2COAlRUVF6tGjR9CVnkTxAa2SmZmpOXPmcIQBASNYlzklljqBFlVWVmr48OGqrKxUdHS06TiAx1wul/r166f169dryJAhpuN0OCY+oAU5OTl6+umnKT0EjOLiYkVHRwdl6UkcZwBuqr6+XkuWLNHWrVtNRwG8JpiXOSWKD7ipN998U9/61rc0YMAA01EAr7AsS7m5uVq5cqXpKMaw1AncgGVZVze1AIFiz549stlsSk5ONh3FGIoPuIH/+Z//UV1dnSZOnGg6CuA1V5Y5g3mHMsUH3MCVaS8khG8TBIYry5zBdlPqr+M4A3Adx44dU2JioioqKhQTE2M6DuAVH3/8sSZNmqTKykomPgBf9eqrr+rJJ5+k9BBQrjyCKJhLT2LiA67R0NCgfv36adOmTYqPjzcdB/CapKQk5eTk6P777zcdxSgmPuBrVqxYocTEREoPAeXQoUM6ffq0Ro0aZTqKcRQf8DWZmZmaO3eu6RiAV+Xl5Wnq1Kls1hLFB3zF9u3bVV1drYcffth0FMCr2M35vyg+4EuysrI0e/ZshYaGmo4CeE1FRYU+++wzjRkzxnQUn0DxAV+orq7Wu+++q/T0dNNRAK/Ky8vTd7/7XYWFcZdKieIDrlq4cKHS0tJ06623mo4CeNWVYwy4jOMMgKSmpib1799f69atU1JSkuk4gNccO3ZMSUlJOnHihDp16mQ6jk9g4gMk5efna8CAAZQeAs7KlSs1ZcoUSu9LKD5AHGFA4GKZ81osdSLolZSUaMqUKTpy5Agv/iOgnDp1SoMGDdLJkydlt9tNx/EZTHwIepmZmZo5cyalh4CTn5+vSZMmUXpfw3c6gtrZs2eVl5enAwcOmI4CeF1eXp5mzJhhOobPYeJDUFu8eLG+853vKDY21nQUwKvOnj2rbdu2adKkSaaj+BwmPgSt5uZm5eTkKDc313QUwOtWr16tCRMmKCoqynQUn8PEh6C1Zs0a9erVS/fee6/pKIDXsZvzxtjViaA1YcIEpaen68knnzQdBfCqCxcuqG/fvqqqquJhytfBxIegtG/fPn388cdKS0szHQXwujVr1ig1NZXSuwFe40NQysrK0owZM7ibBfzemdoG5e6sUvnJGtU4nIqxh2n7xoP6wXf5R92NsNSJoHPhwgX1799fZWVl6t27t+k4QJuUHD2v7M2HteXgaUlSg9N19X1WU4Mi7HaNGxyrWakDldz3FlMxfRLFh6Azf/58bd26VW+++abpKECbLN9aoRfXlcvhbNbNfoLbbJI9LFTzJg/WtJFxHZbP11F8CCoul0uDBg3S0qVLNWrUKNNxALddLr39qm9ytfzBX4gMD9G8yfGU3xfY3IKgsn79enXp0kX33Xef6SiA20qOnteL68rdKj1Jqm9y6cV15dpbdb6dkvkXig9B5cpTGGw2m+kogNuyNx+Ww9ncps91OJuVs/mwlxP5J4oPQePw4cPasWOHHn/8cdNRALedqW3QloOnb/qa3s1YlrTpwGmdrW3wbjA/RPEhaGRnZysjI0ORkZGmowBuy91Z5fE1bJJyd3l+HX/HOT4EnOuda7rj1gj99Z1V2vVRoel4QJuUn6z5ypGFtnA4XSo/cdFLifwXxYeAcbNzTWFyqcu0+XqxsFqzUmM414R25XQ6VVdXp7q6Ol26dOnqf3/91zf67+u9zzHihwrpm+xxthpHkxd+h/6N4kNAaOlck1MhUkiICvadUuHBM5xrCnLNzc1uF5M7pdXc3KyoqChFRUWpc+fOLf53VFSUunXrdsP3de7cWf+v6IwKDnq+KzPGHu6FP0H/RvHB77lzrsmypPqmZr24br8kUX4+qrm5+WqZtEcxOZ3Oq+VyszL68q+/8Y1vtOrjOnfurIiICK/vHB5+MkxbPvVsudMeFqLBvbp4MZV/4gA7/FrJ0fN6fNFW1Te5v8U7MjxUb88YqaQ+LHu6y+VytWsxNTY2ul1M7nyc3W73uyMtZ2obNPqljR4VX0RYiIpeGK9u0RFeTOZ/mPjg17xxrmnBtMB7Hp/L5VJ9fb3Hryvd6H0NDQ2KjIx0q3B69uzZ6mKKjIz0u2Jqb7dFRyj1ru76YP+pNh1psNmkcYO6B33pSRQf/Jg3zzV19A8Dy7LatZgcDofsdrtbxRQbG9vqaSoyMlIhIZyG6mizxw7U3w+dadMKhz0sVLPGDmyHVP6H4oPf8ua5ph+NGfCV/29ZlhwOh1eX77786/r6ekVERLi1fHfbbbe16uOioqIopgCV3PcWzZs8uI336hzMsv4XeI0Pfuv/vL1b+XuOe3wd+4kShe1445rS6tSpk1dfV/p6MYWGhnrhTwHBiKczeIaJD36rxuH0ynWGDL1Xv/nxlGuKKSyMbw/4pmkj45TU5xblbD6sTQdOy6bLh9OvsIeFyNLl1/RmjR3IpPc1fGfDb8XYvfPXt1+vWCUlJXnlWkBHSepzixZMu1dnaxuUu6tK5ScuqsbRpBh7uAb36qK04X3YyHIDFB/81uCeMYoIO8m5JgS1btER17xGjZvj1W/4rbR7+nh8DUtS2nDPrwPAf1B88FtWfY06X6iQXG2b+DjXBAQnig9+x7IsvfXWW0pMTNSwiGrZI9q2Ys+5JiA48Rof/Mrx48f17LPP6pNPPtHq1as1YsQIt+7VeQXnmoDgxcQHv2BZlpYsWaKhQ4dq6NCh2rlzp0aMGCHp8tbueZPjFRkeqpbucmWzXb5H57zJ8ZxrAoIUB9jh8yoqKjRjxgydO3dOixcvVnLy9Z9JtrfqPOeaALSI4oPPcrlcys7O1m9/+1v99Kc/1U9+8pNWHSrnXBOAm6H44JMOHDig6dOny7IsLV68WIMGDTIdCUCA4DU++BSn06mXXnpJo0eP1mOPPabCwkJKD4BXsasTPmPv3r1KT0/XN77xDe3YsUNxcXGmIwEIQEx8MK6hoUG//vWv9Q//8A969tlnVVBQQOkBaDdMfDBq+/btSk9P14ABA1RSUqLevXubjgQgwFF8MOLSpUv69a9/reXLl+vPf/6z/umf/km2lg7hAYAXsNSJDrdlyxYlJyfr+PHjKi0t1eOPP07pAegwTHzoMDU1Nfr5z3+u1atXKycnR9/5zndMRwIQhJj40CHef/99JSYmqrGxUWVlZZQeAGOY+NCuzp07p+eff16FhYVavHixJkyYYDoSgCDHxId2s3LlSiUkJKhr164qLS2l9AD4BCY+eN2pU6c0Z84c7d27VytWrNDo0aNNRwKAq5j44DWWZWn58uVKSkrSgAEDtGfPHkoPgM9h4oNXHD16VDNnzlRVVZXWrVune+65x3QkALguJj54xOVy6dVXX9Xw4cM1cuRIFRcXU3oAfBoTH9rsk08+0fTp03Xp0iVt2rRJCQkJpiMBQIuY+OC25uZm/elPf9K3vvUtTZkyRUVFRZQeAL/BxAe37Nu3TxkZGYqIiNDWrVs1cOBA05EAwC1MfGiVpqYm/du//ZtSU1P19NNPa+PGjZQeAL/ExIcW7d69W+np6erZs6d27typb37zm6YjAUCbMfHhhhwOh375y1/qH//xH/X8889r3bp1lB4Av8fEh+sqKipSRkaG7r77bpWUlKhnz56mIwGAV1B8+Iq6ujr98pe/1IoVK/TKK68oLS3NdCQA8CqWOnHVhg0blJiYqM8//1ylpaWUHoCAxMQHXbhwQf/6r/+q9evXa8GCBZo8ebLpSADQbpj4gty7776rhIQEhYaGqqysjNIDEPCY+ILUmTNn9Nxzz2nbtm1atmyZxo0bZzoSAHQIJr4gY1mW3nnnHSUmJqpHjx4qKSmh9AAEFSa+IHLixAnNmjVLBw4c0KpVqzRy5EjTkQCgwzHxBQHLsvRf//VfSk5OVkJCgnbv3k3pAQhaTHwBrrKyUjNmzNDp06dVUFCgoUOHmo4EAEYx8QUol8ul7Oxs3XPPPRo7dqy2bdtG6QGAmPgC0sGDBzV9+nQ1Nzfrww8/1ODBg01HAgCfwcQXQJxOp15++WWNGjVKaWlpKiwspPQA4GuY+AJEaWmp0tPT1bVrV23fvl133HGH6UgA4JOY+PxcY2OjfvOb32j8+PH60Y9+pA8++IDSA4CbYOLzY8XFxUpPT1dcXJz27Nmj22+/3XQkAPB5THx+qL6+Xj/96U81ZcoU/eIXv9Dq1aspPQBoJYrPzxQWFiopKUlHjx5VaWmpnnzySdlsNtOxAMBvsNTpJy5evKif//znys/PV3Z2th555BHTkQDALzHx+YH169crISFB9fX1Kisro/QAwANMfD7s888/149//GNt2rRJixYt0sSJE01HAgC/x8Tno1atWqWEhARFRUWptLSU0gMAL2Hi8zHV1dWaO3eudu/erbfeeksPPPCA6UgAEFCY+HyEZVl6/fXXlZiYqLi4OJWUlFB6ANAOmPh8QFVVlWbOnKnPPvtMa9eu1b333ms6EgAELCY+gyzL0qJFizRs2DClpKRox44dlB4AtDMmPkM+/fRTPfPMM7p48aI2bdqkhIQE05EAICgw8XWw5uZm/fnPf9aIESM0adIkFRUVUXoA0IGY+DrQ/v37lZGRobCwMH300Ue68847TUcCgKDDxNcBmpqa9O///u964IEHNG3aNG3evJnSAwBDmPja2e7du5Wenq7Y2Fjt3LlT/fr1Mx0JAIIaE187cTgcmjdvnh566CE999xzev/99yk9APABTHzt4KOPPlJ6erri4+NVUlKiXr16mY4EAPgCxedFdXV1+tWvfqW33npLr7zyitLS0nhWHgD4GJY6vWTjxo1KSkrS6dOnVVpaqkcffZTSAwAfxMTnoQsXLuhnP/uZ1q1bpwULFujhhx82HQkAcBNMfB5Yu3bt1cPnZWVllB4A+AEmvjY4e/asnnvuOX300UdaunSpxo8fbzoSAKCVmPjcYFmWVqxYoYSEBHXv3l179+6l9ADAzzDxtdKJEyc0e/ZslZeXa+XKlbrvvvtMRwIAtAETXwssy9Jrr72m5ORkxcfHa9euXZQeAPgxJr6b+OyzzzRjxgydOnVK69ev17Bhw0xHAgB4iInvOlwul3JycjR8+HA98MAD2r59O6UHAAGCie9rDh06pOnTp6uxsVGFhYUaMmSI6UgAAC9i4vuC0+nUH//4R91333363ve+pw8//JDSA4AAxMSny4fP09PTFR0drW3btmnAgAGmIwEA2klQT3yNjY367W9/q3Hjxmn69OnasGEDpQcAAS5oJ74dO3YoPT1d3/zmN7V792716dPHdLB3fnsAAAQmSURBVCQAQAcIuomvvr5eL7zwgh5++GG98MILevfddyk9AAgiQTXx/f3vf1dGRoaGDh2qvXv3qkePHqYjAQA6WFAU38WLF/WLX/xCq1atUlZWlr73ve+ZjgQAMCTglzo/+OADJSYmqq6uTmVlZZQeAAS5gJ34Pv/8c/3kJz/Rhg0btHDhQj300EOmIwEAfEBATnx/+9vflJiYqMjISJWVlVF6AICrAmriO336tObOnaudO3fq9ddfV2pqqulIAAAfExATn2VZeuONN5SYmKi+ffuqpKSE0gMAXJffT3zHjh3TzJkzdeTIEa1evVojRowwHQkA4MP8duKzLEv/+Z//qaFDh2r48OHauXMnpQcAaJFfTnxHjhzRM888o/Pnz2vDhg1KSkoyHQkA4Cf8auJrbm7W/PnzlZKSookTJ2rr1q2UHgDALX4z8ZWXlysjI0MhISEqKirSXXfdZToSAMAP+fzE19TUpP/4j//Q/fffryeeeEJbtmyh9AAAbebTE9+ePXuUnp6u2267TTt27FBcXJzpSAAAP9fuxXemtkG5O6tUfrJGNQ6nYuxhGtwzRo/e00fdoiOu+zkNDQ363e9+p4ULF+qll17SD3/4Q9lstvaOCgAIAjbLsqz2uHDJ0fPK3nxYWw6eliQ1OF1X32cPC5Elaeyg7pqVOlDJfW+5+r6tW7cqIyNDd955p3JyctS7d+/2iAcACFLtUnzLt1boxXXlcjibdbOr22ySPSxU8yYP1tSkWP3qV7/SG2+8ofnz5+uxxx5jygMAeJ3Xi+9y6e1XfZOr5Q/+QqcQqWn727qvu1Pz589X9+7dvRkJAICrvFp8JUfP6/FFW1Xf1Oz254aHWMp79n4l9bml5Q8GAKCNvHqcIXvzYTmc7peeJDktm3I2H/ZmHAAAruG14jtT26AtB0/f9DW9m7EsadOB0zpb2+CtSAAAXMNrxZe7s8rja9gk5e7y/DoAANyI14qv/GTNV44stIXD6VL5iYteSgQAwLW8Vnw1DqeXrtPklesAAHA9Xiu+GLt3bgITYw/3ynUAALgerxXf4J4xigjz7HL2sBAN7tXFS4kAALiW14ov7Z4+Hl/DkpQ23PPrAABwI14rvtuiI5R6V3e19S5jNps0blD3G964GgAAb/DqAfbZYwfKHhbaps+1h4Vq1tiB3owDAMA1vFp8yX1v0bzJgxUZ7t5lI8NDNG/yYG5XBgBod15/Ht+0kXGS5PbTGa58HgAA7andnse3t+q8cjYf1qYDp2XT5cPpV1x5Ht+4Qd01a+xAJj0AQIdpt+K74mxtg3J3Van8xEXVOJoUYw/X4F5dlDb8xk9gBwCgvbR78QEA4Eu8urkFAABfR/EBAIIKxQcACCoUHwAgqFB8AICgQvEBAIIKxQcACCoUHwAgqFB8AICg8v8BKvmDqC4t4JIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# define graph object\n",
    "\n",
    "e = [(1,2),(1,4),(1,5),(2,3),(3,4)]\n",
    "G = nx.Graph(e)\n",
    "pos = nx.spring_layout(G)\n",
    "\n",
    "# choose weigths\n",
    "for (u, v) in G.edges():\n",
    "    G.edges[u,v]['weight'] = 1.0 #random.uniform(0, 1)\n",
    "# draw graph\n",
    "nx.draw(G, pos)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# set Ising matrix \n",
    "J = np.array([[0., 1., 0., 1., 1.],[1., 0., 1., 0., 0.],[0., 1., 0., 1., 0.],[1., 0., 1., 0., 0.],[1., 0., 0., 0., 0.]])\n",
    "\n",
    "# plot Ising matrix\n",
    "plt.figure(1, figsize=[7, 5])\n",
    "sns.heatmap(J, annot=True,  linewidths=.5, cmap=\"YlGnBu\", annot_kws = {'alpha': 1})\n",
    "plt.title('Ising distance matrix');\n",
    "plt.tight_layout();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## QAOA circuit builder functions  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# function to implement evolution with driver Hamiltonian\n",
    "def driver(beta, n_qubits):\n",
    "    \"\"\"\n",
    "    Returns circuit for driver Hamiltonian U(Hb, beta)\n",
    "    \"\"\"\n",
    "    # instantiate circuit object\n",
    "    circ = Circuit()\n",
    "\n",
    "    for qubit in range(n_qubits):\n",
    "        gate = Circuit().rx(qubit, 2*beta)\n",
    "        circ.add(gate)\n",
    "\n",
    "    return circ\n",
    "\n",
    "\n",
    "# helper function for evolution with cost Hamiltonian\n",
    "def cost_circuit(gamma, n_qubits, ising, device):\n",
    "    \"\"\"\n",
    "    returns circuit for evolution with cost Hamiltonian\n",
    "    \"\"\"\n",
    "    # instantiate circuit object\n",
    "    circ = Circuit()\n",
    "\n",
    "    # get all non-zero entries (edges) from Ising matrix\n",
    "    idx = ising.nonzero()\n",
    "    edges = list(zip(idx[0], idx[1]))\n",
    "\n",
    "    # apply ZZ gate for every edge (with corresponding interation strength)\n",
    "    for qubit_pair in edges:\n",
    "        # get interaction strength from Ising matrix\n",
    "        int_strength = ising[qubit_pair[0], qubit_pair[1]]\n",
    "        # for Rigetti we decompose ZZ using CNOT gates\n",
    "        if device.name == 'Aspen-8':\n",
    "            gate = ZZgate(qubit_pair[0], qubit_pair[1], gamma*int_strength)\n",
    "            circ.add(gate)\n",
    "        # classical simulators and IonQ support ZZ gate\n",
    "        else:\n",
    "            gate = Circuit().zz(qubit_pair[0], qubit_pair[1], angle=2*gamma*int_strength)\n",
    "            circ.add(gate)\n",
    "\n",
    "    return circ\n",
    "\n",
    "# function that computes cost function for given params\n",
    "def objective_function(params, device, ising, n_qubits, n_shots, tracker, s3_folder, verbose):\n",
    "    \"\"\"\n",
    "    objective function takes a list of variational parameters as input,\n",
    "    and returns the cost associated with those parameters\n",
    "    \"\"\"\n",
    "\n",
    "    if verbose:\n",
    "        print('==================================' * 2)\n",
    "        print('Calling the quantum circuit. Cycle:', tracker['count'])\n",
    "\n",
    "    # get a quantum circuit instance from the parameters\n",
    "    qaoa_circuit = circuit(params, device, n_qubits, ising)\n",
    "   \n",
    "    # classically simulate the circuit\n",
    "    # execute the correct device.run call depending on whether the backend is local or cloud based\n",
    "    if device.name == 'DefaultSimulator':\n",
    "        task = device.run(qaoa_circuit, shots=n_shots)\n",
    "    else:\n",
    "        task = device.run(qaoa_circuit, s3_folder,\n",
    "                          shots=n_shots, poll_timeout_seconds=3*24*60*60)\n",
    "\n",
    "    # get result for this task\n",
    "    result = task.result()\n",
    "\n",
    "    # get metadata\n",
    "    metadata = result.task_metadata\n",
    "\n",
    "    # convert results (0 and 1) to ising (-1 and 1)\n",
    "    meas_ising = result.measurements\n",
    "    meas_ising[meas_ising == 0] = -1\n",
    "\n",
    "    # get all energies (for every shot): (n_shots, 1) vector\n",
    "    all_energies = np.diag(np.dot(meas_ising, np.dot(ising, np.transpose(meas_ising))))\n",
    "\n",
    "    # find minimum and corresponding classical string\n",
    "    energy_min = np.min(all_energies)\n",
    "    tracker['opt_energies'].append(energy_min)\n",
    "    optimal_string = meas_ising[np.argmin(all_energies)]\n",
    "    tracker['opt_bitstrings'].append(optimal_string)\n",
    "\n",
    "    # store optimal (classical) result/bitstring\n",
    "    if energy_min < tracker['optimal_energy']:\n",
    "        tracker.update({'optimal_energy': energy_min})\n",
    "        tracker.update({'optimal_bitstring': optimal_string})\n",
    "\n",
    "    # store global minimum\n",
    "    tracker['global_energies'].append(tracker['optimal_energy'])\n",
    "\n",
    "    # energy expectation value\n",
    "    energy_expect = np.sum(all_energies) / n_shots\n",
    "    \n",
    "    if verbose:\n",
    "        print('Minimal energy:', energy_min)\n",
    "        print('Optimal classical string:', optimal_string)\n",
    "        print('Energy expectation value (cost):', energy_expect)\n",
    "\n",
    "    # update tracker\n",
    "    tracker.update({'count': tracker['count']+1, 'res': result})\n",
    "    tracker['costs'].append(energy_expect)\n",
    "    tracker['params'].append(params)\n",
    "\n",
    "    return energy_expect\n",
    "\n",
    "\n",
    "# The function to execute the training: run classical minimization.\n",
    "def train(device, options, p, ising, n_qubits, n_shots, opt_method, tracker, s3_folder, verbose=True):\n",
    "    \"\"\"\n",
    "    function to run QAOA algorithm for given, fixed circuit depth p\n",
    "    \"\"\"\n",
    "    print('Starting the training.')\n",
    "\n",
    "    print('==================================' * 2)\n",
    "    print(f'OPTIMIZATION for circuit depth p={p}')\n",
    "\n",
    "    if not verbose:\n",
    "        print('Param \"verbose\" set to False. Will not print intermediate steps.')\n",
    "        print('==================================' * 2)\n",
    "\n",
    "    # initialize\n",
    "    cost_energy = []\n",
    "\n",
    "    # randomly initialize variational parameters within appropriate bounds\n",
    "    gamma_initial = np.random.uniform(0, 2 * np.pi, p).tolist()\n",
    "    beta_initial = np.random.uniform(0, np.pi, p).tolist()\n",
    "    params0 = np.array(gamma_initial + beta_initial)\n",
    "\n",
    "    # set bounds for search space\n",
    "    bnds_gamma = [(0, 2 * np.pi) for _ in range(int(len(params0) / 2))]\n",
    "    bnds_beta = [(0, np.pi) for _ in range(int(len(params0) / 2))]\n",
    "    bnds = bnds_gamma + bnds_beta\n",
    "\n",
    "    tracker['params'].append(params0)\n",
    "\n",
    "    # run classical optimization (example: method='Nelder-Mead')\n",
    "    result = minimize(\n",
    "            objective_function, params0, \n",
    "            args=(device, ising, n_qubits, n_shots, tracker, s3_folder, verbose),\n",
    "            options=options, method=opt_method, bounds=bnds\n",
    "        )\n",
    "\n",
    "    # store result of classical optimization\n",
    "    result_energy = result.fun\n",
    "    cost_energy.append(result_energy)\n",
    "    print('Final average energy (cost):', result_energy)\n",
    "    result_angle = result.x\n",
    "    print('Final angles:', result_angle)\n",
    "    print('Training complete.')\n",
    "\n",
    "    return result_energy, result_angle, tracker\n",
    "\n",
    "# function to build the QAOA circuit with depth p\n",
    "def circuit(params, device, n_qubits, ising):\n",
    "    \"\"\"\n",
    "    function to return full QAOA circuit; depends on device as ZZ implementation depends on gate set of backend\n",
    "    \"\"\"\n",
    "\n",
    "    # initialize qaoa circuit with first Hadamard layer: for minimization start in |->\n",
    "    circ = Circuit()\n",
    "    X_on_all = Circuit().x(range(0, n_qubits))\n",
    "    circ.add(X_on_all)\n",
    "    H_on_all = Circuit().h(range(0, n_qubits))\n",
    "    circ.add(H_on_all)\n",
    "\n",
    "    # setup two parameter families\n",
    "    circuit_length = int(len(params) / 2)\n",
    "    gammas = params[:circuit_length]\n",
    "    betas = params[circuit_length:]\n",
    "\n",
    "    # add QAOA circuit layer blocks\n",
    "    for mm in range(circuit_length):\n",
    "        circ.add(cost_circuit(gammas[mm], n_qubits, ising, device))\n",
    "        circ.add(driver(betas[mm], n_qubits))\n",
    "\n",
    "    return circ\n",
    "# helper function to plot graph\n",
    "def plot_colored_graph_simple(graph, colors, pos):\n",
    "    \"\"\"\n",
    "    plot colored graph for given colored solution\n",
    "    \"\"\"\n",
    "\n",
    "    # define color scheme\n",
    "    colorlist = ['#e41a1c', '#377eb8', '#4daf4a', '#984ea3', '#ff7f00', '#ffff33', '#a65628', '#f781bf']\n",
    "\n",
    "    # draw network\n",
    "    nx.draw_networkx(graph, pos, node_color=[colorlist[colors[int(node)-1]] for node in graph.nodes],\n",
    "                     node_size=400, font_weight='bold', font_color='w')\n",
    "\n",
    "    # plot the graph\n",
    "    plt.axis('off');\n",
    "    # plt.savefig(\"./figures/weighted_graph.png\") # save as png\n",
    "    # plt.show();\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Setup QAOA classical optimizer and initial parameters "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SV1\n"
     ]
    }
   ],
   "source": [
    "##################################################################################\n",
    "# set up hyperparameters\n",
    "##################################################################################\n",
    "\n",
    "# User-defined hypers\n",
    "DEPTH = 3  # circuit depth for QAOA\n",
    "SHOTS = 100  # number measurements to make on circuit\n",
    "OPT_METHOD = 'Powell'  # SLSQP, COBYLA, Nelder-Mead, BFGS, Powell, ...\n",
    "\n",
    "# set up the problem\n",
    "n_qubits = J.shape[0]\n",
    "\n",
    "# initialize reference solution (simple guess)\n",
    "bitstring_init = -1 * np.ones([n_qubits])\n",
    "energy_init = np.dot(bitstring_init, np.dot(J, bitstring_init))\n",
    "\n",
    "# set tracker to keep track of results\n",
    "tracker = {\n",
    "    'count': 1,                           # Elapsed optimization steps\n",
    "    'optimal_energy': energy_init,        # Global optimal energy\n",
    "    'opt_energies': [],                   # Optimal energy at each step\n",
    "    'global_energies': [],                # Global optimal energy at each step\n",
    "    'optimal_bitstring': bitstring_init,  # Global optimal bitstring\n",
    "    'opt_bitstrings': [],                 # Optimal bitstring at each step\n",
    "    'costs': [],                          # Cost (average energy) at each step\n",
    "    'res': None,                          # Quantum result object\n",
    "    'params': []                          # Track parameters\n",
    "}\n",
    "\n",
    "# set options for classical optimization\n",
    "options = {'disp': True, 'maxiter': 500}\n",
    "verbose = False\n",
    "# options = {'disp': True, 'ftol': 1e-08, 'maxiter': 100, 'maxfev': 50}  # example options\n",
    "print(device.name)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Run QAOA "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Circuit depth hyperparameter: 3\n",
      "Problem size: 5\n",
      "Starting the training.\n",
      "====================================================================\n",
      "OPTIMIZATION for circuit depth p=3\n",
      "Param \"verbose\" set to False. Will not print intermediate steps.\n",
      "====================================================================\n",
      "Optimization terminated successfully.\n",
      "         Current function value: -5.560000\n",
      "         Iterations: 3\n",
      "         Function evaluations: 361\n",
      "Final average energy (cost): -5.56\n",
      "Final angles: [2.41662901 3.71746029 3.42486989 2.37384711 1.24584151 1.72729949]\n",
      "Training complete.\n",
      "Code execution time [sec]: 970.8628726005554\n",
      "Optimal energy: -10.0\n",
      "Optimal classical bitstring: [ 1 -1  1 -1 -1]\n",
      "Minimal energy found with QAOA: -10.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "##################################################################################\n",
    "# run QAOA optimization on graph \n",
    "##################################################################################\n",
    "\n",
    "print('Circuit depth hyperparameter:', DEPTH)\n",
    "print('Problem size:', n_qubits)\n",
    "\n",
    "# kick off training\n",
    "start = time.time()\n",
    "result_energy, result_angle, tracker = train(\n",
    "    device = device, options=options, p=DEPTH, ising=J, n_qubits=n_qubits, n_shots=SHOTS, \n",
    "    opt_method=OPT_METHOD, tracker=tracker, s3_folder=s3_folder, verbose=verbose)\n",
    "end = time.time()\n",
    "\n",
    "# print execution time\n",
    "print('Code execution time [sec]:', end - start)\n",
    "\n",
    "# print optimized results\n",
    "print('Optimal energy:', tracker['optimal_energy'])\n",
    "print('Optimal classical bitstring:', tracker['optimal_bitstring'])\n",
    "\n",
    "# visualize solution\n",
    "colorlist = tracker['optimal_bitstring']\n",
    "colorlist[colorlist == -1] = 0\n",
    "\n",
    "#plot_colored_graph(J, N, colorlist, pos)\n",
    "plot_colored_graph_simple(G, colorlist, pos)\n",
    "print('Minimal energy found with QAOA:', tracker['optimal_energy'])"
   ]
  }
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